Scanning interferometry for thin film thickness and surface measurements

ABSTRACT

A method including: providing a low coherence scanning interferometry data for at least one spatial location of a sample having multiple interfaces, wherein the data is collected using a low coherence scanning interferometer having an illumination geometry and an illumination frequency spectrum, and wherein the data comprises a low coherence scanning interferometry signal having multiple regions of fringe contrast corresponding to the multiple interfaces; and determining a distance between at least one pair of interfaces based on a distance between the corresponding regions of fringe contrast and information about the illumination geometry.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.10/974,466, entitled “SCANNING INTERFEROMETRY FOR THIN FILM THICKNESSAND SURFACE MEASUREMENTS,” filed on Oct. 27, 2004, now U.S. Pat. No.7,324,210, which claims priority under 35 U.S.C. 119(e) to U.S.Provisional Patent Application: U.S. Patent Application Ser. No.60/515,140 filed Oct. 27, 2003 and entitled “THIN FILM THICKNESS ANDSIMULTANEOUS SURFACE TOPOGRAPHY MEASUREMENT USING SCANNINGINTERFEROMETRY,” by Peter J. de Groot et al., the contents both of whichare incorporated herein by reference.

BACKGROUND

The invention relates to using scanning interferometry to measurethickness(es), surface topography, and/or other characteristics ofobjects having complex surface structures, such as thin film(s).

Interferometric techniques are commonly used to measure the profile of asurface of an object. To do so, an interferometer combines a measurementwavefront reflected from the surface of interest with a referencewavefront reflected from a reference surface to produce aninterferogram. Fringes in the interferogram are indicative of spatialvariations between the surface of interest and the reference surface.

A scanning interferometer scans the optical path length difference (OPD)between the reference and measurement legs of the interferometer over arange comparable to, or larger than, the coherence length of theinterfering wavefronts, to produce a scanning interferometry signal foreach camera pixel used to measure the interferogram. A limited coherencelength can be produced, for example, by using a white-light source,which is referred to as scanning white light interferometry (SWLI). Atypical scanning white light interferometry (SWLI) signal is a fewfringes localized near the zero optical path difference (OPD) position.The signal is typically characterized by a sinusoidal carrier modulation(the “fringes”) with bell-shaped fringe-contrast envelope. Theconventional idea underlying SWLI metrology is to make use of thelocalization of the fringes to measure surface profiles. Scanninginterferometers that use a limited coherence length to localizeinterference fringes in the interferometry signal are also referred toas “low coherence scanning interferometers.”

Typically, there are two approaches to processing such data. The firstapproach is to locate the peak or center of the envelope, assuming thatthis position corresponds to the zero optical path difference (OPD) of atwo-beam interferometer for which one beam reflects from the objectsurface. The second approach is to transform the signal into thefrequency domain and calculate the rate of change of phase withwavelength, assuming that an essentially linear slope is directlyproportional to object position. See, for example, U.S. Pat. No.5,398,113 to Peter de Groot. This latter approach is referred to asFrequency Domain Analysis (FDA).

If a low coherence scanning interferometer is used to collect a scanninginterferometry signal from a sample having a thin film (e.g., a simplesingle-layer partially reflective film over an opaque substrate), and ifthe film is sufficiently thick, then the scanning interferometry signalwill include two distinct regions of fringes corresponding to the upperand lower interfaces of the film. This is shown in FIG. 1, extractedfrom a reference by S. Petitgrand et al. (S. Petitgrand, A. Bosseboeuf,J. P. Gilles, P. Coste, P. Nérin, P. Vabre “Mesures 3D de topographieset de vibrations à l'échelle (sub)micrométrique par microscopie optiqueinterférométrique” Proc. Club CMOI, Méthodes et Techniques Optiques pourl'Industrie (2002). A nearly identical paper can be downloaded fromFogale Nanotech website(http://www.fogale.com/acrobat/IEFCMOI2002_FR.pdf)). According toanother paper by Bosseboeuf and Petigrand (Proc. SPIE 5145, 1-16,(2003)), the distance between these two signals is “Δ=n₁d,” where here Δis the distance between the maxima of the two regions of fringecontrast, d is the physical film thickness and n₁ is the index ofrefraction.

Because the light passes through the film before reaching the substrate,there is a distortion in the apparent film thickness related to therefractive properties of the film. In prior-art references such asBosseboeuf and Petigrand, the correction for this effect is to dividethe apparent thickness by the index of refraction, to recover the truephysical thickness of the film. Unfortunately, we often observe thatthis correction is insufficient.

In other applications, one is interested in the topology of the topand/or bottom surface of the film, instead or, or in addition to, thethickness of the thin film. Unfortunately, conventional processing ofthe low coherence scanning interferometry data can sometimes becorrupted by the presence of one or more underlying layers.

SUMMARY

The inventors have recognized that an accurate analysis of low coherencescanning interferometry data of a sample having one or more layers(e.g., a thin film sample) should take into account both theillumination frequency spectrum and the illumination geometry (e.g., thenumerical aperture of the light used to illuminate the sample) to moreaccurately account for the low coherence phenomenon that produce theregions of fringe contrast. For example, in addition to the lowcoherence phenomenon resulting from a broadband light source, the lowcoherence can also result from using a high numerical aperture (NA) fordirecting light to, and/or receiving light from, the test object. Thehigh NA causes light rays to contact the test surface over a range ofangles, and generates different spatial frequency components in therecorded signal as the OPD is scanned. The separation of the regions offringe contrast in a signal produced from a multilayer sample willdepend on the relative strengths of such low coherence phenomena.

For example, the inventors have discovered that in the limit of very lowNA and white light illumination, the apparent thickness of a thin filmsample based on the separation between regions of the fringe contrast inthe low coherence scanning interferometry signal is corrected bydividing this apparent thickness by the group-velocity index ofrefraction. In the opposite limit of very high NA and monochromaticillumination, the apparent thickness is corrected by multiplying it bythe index of refraction.

For intermediate illumination conditions, where both broadbandillumination and high NA contribute the localization of interferencefringes, the correction of the apparent thickness based on theseparation between regions of the fringe contrast can be determinedbased on a theoretical model (described in further detail below) thatmore accurately takes into account both phenomena. In practice theresults of the model can be represented as a look-up table or simplifiedfunction which provides a correction factor to a user as a function ofinput parameters related to the illumination geometry and illuminationfrequency spectrum.

In another aspect, the inventors have recognized that the illuminationconditions can be selected to suppress the region(s) of fringe contrastin the interferometry signal associated with an underlying layer orlayers of a sample. As a result, the interferometry signal is dominatedonly by the fringe contrast region associated with the top surface ofthe sample, and subsequent processing of the interferometry signalusing, for example, conventional techniques to more accurately providesurface profile information about the top surface. This phenomenontypically occurs when there is both broadband illumination (e.g., abandwidth larger than about 100 nm in the visible) and high NA (e.g.,greater than about 0.5, and preferably greater than 0.7). In certainembodiments, an objective for the low coherence scanning interferometercan be selected to provide such high NA, while also providing a lowmagnification (e.g., less than 10×) to provide a large field of view.

We now generally summarize different aspects and features of theinvention.

In general, in one aspect, the invention features a method including:(i) providing a low coherence scanning interferometry data for at leastone spatial location of a sample having multiple interfaces, wherein thedata is collected using a low coherence scanning interferometer havingan illumination geometry and an illumination frequency spectrum, andwherein the data includes a low coherence scanning interferometry signalhaving multiple regions of fringe contrast corresponding to the multipleinterfaces; and (ii) determining a distance between at least one pair ofinterfaces based on a distance between the corresponding regions offringe contrast and information about the illumination geometry and/orthe illumination frequency spectrum.

Embodiments of the method may include any of the following features.

Determining the distance between at least a pair of the interfacesincludes providing information about a correspondence between thedistance between the pair of interfaces and the distance between thecorresponding regions of fringe contrast in the interferometry signalfor different settings of the illumination geometry and the illuminationfrequency spectrum. For example, the correspondence may be representedas a function or a look-up table that uses the information about theillumination geometry and/or the illumination frequency spectrum asinput parameters.

The correspondence may be based on a theoretical model for theinterferometer that uses the information about the illumination geometryand the illumination frequency spectrum as input parameters.

For example, the theoretical model may be based on the followingexpression for the interferometry signal I(ζ) as a function of scancoordinate ζ for each spatial location in the data:

I(ζ) = ∫₀^(∞)∫₀¹g(β, k, ζ)U(β)V(k)β 𝕕β 𝕕kwhere U is an illumination distribution in a pupil plane of an objectiveused to illuminate the sample as a function of directional cosine β, Vis the illumination frequency spectrum as a function of spectralwavenumber k, andg(β,k,ζ)=R+Z+2√{square root over (RZ)} cos[2βk(h−ζ)+(υ−ω)]for a reference path reflectivity R, a sample path reflectivity Z, and alocal sample height h, and where phase offsets υ, ω are system and phasechange on reflection values for the reference and sample paths,respectively.

The distance between the pair of interfaces may be determined bydetermining an estimate for the distance between the pair of interfacescorresponding to the distance between the two regions of fringecontrast, and correcting the estimate based on the information about theillumination geometry and the frequency spectrum. For example, thecorrection of the initial estimate may include decreasing the estimateby a scale factor that increases with a group velocity index of thefilm. In another example, the correction of the initial estimate mayinclude increasing the estimate by a scale factor that increases with arefractive index of the film.

The sample may be a thin film sample, where the pair of interfaces is atop and bottom surface of the film. The sample may have the film at somespatial locations and not others.

The sample may include a spacer element in a liquid crystal cell.

The sample may include a solder bump.

In general, in another aspect, the invention features an apparatusincluding: a low coherence scanning interferometer configured to collectdata for at least one spatial location of a sample having at least onefilm, the coherence scanning interferometer having an illuminationgeometry and an illumination frequency spectrum, and the data includinga low coherence scanning interferometry signal having multiple regionsof fringe contrast corresponding to the multiple interfaces; and anelectronic processor configured to analyze the data and determine adistance between at least one pair of interfaces based on a distancebetween the corresponding regions of fringe contrast and informationabout the illumination geometry and/or the illumination frequencyspectrum.

Embodiments of the apparatus may include any of the following features.

The low coherence interferometer may be configured for use with anadjustable numerical aperture for the illumination geometry, and theinformation about the illumination geometry may include informationabout which numerical aperture was used to collect the interferometrysignal. For example, the apparatus may further include a plurality ofinterference objective having different numerical apertures (NAs) eachconfigured for use in the low coherence scanning interferometer toprovide the adjustable numerical aperture for the illumination geometry.

Alternatively, or in addition, the low coherence interferometer may beconfigured for use with an adjustable illumination frequency spectrum,and the information about the illumination geometry may includeinformation about which illumination frequency spectrum was used tocollect the interferometry signal. For example, the apparatus mayinclude a plurality of light sources (e.g., light emitting diodes(LEDs)) having different emission spectrums each configured for use inthe low coherence scanning interferometer to provide the adjustableillumination frequency spectrum.

The electronic processor in the apparatus may also include featurescorresponding to those described above for the method aspect.

In general, in another aspect, the invention features a methodincluding: using a low coherence scanning interferometer having anillumination geometry and an illumination frequency spectrum to collecta low coherence scanning interferometry signal for each of multiplespatial locations of a sample having at least one thin film with a topsurface and a bottom surface; selecting the illumination geometry andthe illumination frequency spectrum to suppress a region of fringecontrast in the signals corresponding to the bottom surface relative toa region of fringe contrast in the signals corresponding to the topsurface; and determining a surface height profile for the top surface ofthe film based on the signals.

Embodiments of the method may include any of the following features.

The selected illumination geometry may include an objective toilluminate the sample with a numerical aperture greater than 0.5, orpreferably greater than 0.7, or even more preferably, greater than 0.8.In some cases, the objective has a magnification less than 10× toimprove the field of view.

The sample may include a spacer element in a liquid crystal cell.

The sample may include a solder bump.

In general, in another aspect, the invention features a low coherencescanning interferometer having an objective to illuminate the samplewith a numerical aperture greater than 0.5 and a magnification less than10×. For example, the numerical aperture may be greater than 0.7, ormore preferably greater than 0.8.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. In case of conflict withpublications, patent applications, patents, and other referencesmentioned incorporated herein by reference, the present specification,including definitions, will control.

Other features, objects, and advantages of the invention will beapparent from the following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph showing a typical low coherence interferometry signalfor a thin film sample.

FIG. 2 is a flow chart showing an interferometry method for determininga thickness of a layer in a sample having one or more layers.

FIG. 3 is a schematic drawing of a Linnik-type scanning interferometer.

FIG. 4 is a schematic drawing of a Mirau-type scanning interferometer.

FIG. 5 is a diagram showing illumination of the test sample through anobjective lens.

FIGS. 6( a) and 6(b) show simulations of a low-coherence scanninginterferometry signal based on the model disclosed herein for a 2-μmthick film of index 2 deposited on a substrate of index 4, viewed with a500-nm center wavelength. FIG. 6( a) is for a broad 200-nm gaussianbandwidth, and narrow 0.28 NA illumination. FIG. 6( b) is for a narrow5-nm bandwidth, and wide 0.80 NA illumination.

FIG. 7( a) is a graph showing agreement between the interferometrysignal predicted by the model and experimental data for a SiC flat. FIG.7( b) is a graph showing agreement between the interferometry signalpredicted by the model and experimental data for a thin film standard of1025 nm of SiO₂ on Si.

FIGS. 8( a) and 8(b) are graphs showing the agreement of the data inFIG. 7( b) in the frequency domain.

FIG. 9 is a graph of simulated interferometry signal for a 2-μm thickfilm of index n′=2 deposited on a substrate of index 4, viewed with a500-nm center wavelength, 0.35 NA and 60-nm bandwidth. The left-handpeak is at about −3.75 microns, or 7n′L/8, where L is the thickness ofthe film.

FIG. 10 is a graph of a simulated interferometry signal for an L=2-μmthick film of index n′=2 deposited on a substrate of index 4, viewedwith a 500-nm center wavelength, 0.8 NA and 200-nm bandwidth. Thecombination of broad spectral bandwidth and high NA suppresses theunderlying reflection from the substrate so that the top surface can bemore easily analyzed.

FIGS. 11 a and 11 b are exemplary structures having copperinterconnects. FIGS. 11 a and 11 b show the structure before and afterplanarization, respectively.

FIGS. 12 a and 12 b are exemplary structures formed during solder bumpprocessing.

FIG. 12 a shows the structure before addition of solder. FIG. 12 b showsthe structure after addition of solder but prior to flowing the solder.

FIG. 13 is a portion of an exemplary liquid crystal display.

Like reference numerals in different drawings refer to common elements.

DETAILED DESCRIPTION

The invention features a method to accurately correct the distortion inthe apparent film thickness as measured by a low-coherence interferencemicroscope by taking into account the coherence effects related to theillumination geometry. In preferred embodiments, the correction can beby means of a formula or look up table based in part on the NA of theobjective and the nominal spectral characteristics of the source light.FIG. 2 is flow chart providing an exemplary sequence of steps for themethod.

In step 290, an interference microscope provides a scanning interferencesignal from each of different surface locations of a sample having oneor more layers. The interference microscope is a low-coherence(spectrally broadband and/or extended source) interferometer. Theinterferometer is used to mechanically or electro-optically scan theoptical path difference (OPD) between a reference and measurement path,the measurement path being directed to an object surface. For example,scanning an interference objective along the line of the surface heightcoordinate generates an interference signal with a localized fringecontrast. A computer records an interference intensity signal during theOPD scan for each of multiple camera pixels corresponding to thedifferent surface locations of the sample. The apparatus is configuredto analyze surfaces that may have one or more layers (e.g., a partiallyreflective thin film on a substrate) for which multiple interferencesignals are generated in sequence during the scan, corresponding to theinterfaces at the surface and between layers.

In step 292, the scanning interference signal from the differentlocations are analyzed to identify regions of fringe contrast associatedwith each reflective or partially reflective interface in the sample.Typically, this done computationally. The center location of each regionof fringe contrast can be identified using conventional methods, such asidentifying the peak in the fringe contrast envelope, identifying thecentroid of the fringe, or using frequency domain analysis (FDA). Forexample, when using FDA, each of region of fringe contrast is Fouriertransformed and the center of each fringe contrast region is determinedfrom the slope of the phase of the Fourier transform with respect towavevector. In further embodiments, techniques that account for systemdispersion characteristics can be used to more accurately determine thefringe contrast positions in the scanning interferometry data. Suitabletechniques are disclosed in U.S. patent application Ser. No. 10/941,651entitled “SURFACE PROFILING USING AN INTERFERENCE PATTERN MATCHINGTEMPLATE” by Peter J. de Groot and filed Sep. 15, 2004, the contents ofwhich are incorporated herein by reference. The center position of eachregion of fringe contrast in the scanning interferometry signal providean initial estimate for the relative position of each reflective orpartially reflective interface in the sample.

In step 294, correction factors are applied to the estimates determinedin step 292, to more accurately determine the physical distance betweenthe interfaces of the relevant film layer (e.g., the actual thickness ofa thin film layer). For example, the correction factor can be a scalingfactor that converts the scanning distance between respective regions offringe contrast extracted in step 292 to the physical distance betweenthe interfaces of the relevant film layer. The correction factor can beapplied to the scanning distances for each spatial location in theinterferometry data to provide a thickness profile for each layer of thesample. Also, the thicknesses determined for different spatial locationscan be averaged to improve signal-to-noise. Furthermore, the dataextracted in step 292 can be laterally smoothed before applying thecorrection factor(s) and/or determining the thickness measurement(s).

In step 296, the resulting thickness value(s) or profile(s) can shown ona user display and/or directed to another process as part of a qualitycontrol feedback loop (e.g., to determine whether, for example, achemical mechanical processing step, solder bump thickness, or liquidcrystal spacer thickness, has been optimized).

The correction factors themselves are determined in step 298, based oninput parameters that include the geometric and spectral characteristics(i.e., the illumination geometry and illumination frequency spectrum) ofthe instrument used to collect the data in step 290. The inputparameters may also include the refractive index dispersion of the filmlayers. The correction factors may be based on direct calculations usinga theoretical model for the low coherence interferometry signal (whichis described further below). Alternatively, the correction factors maybe determined from a look-up table or simplified function that is basedon the theoretical model for typical values of the illumination geometryand illumination frequency spectrum for the interferometer used tocollect the data in step 290. Whatever the exact implementation, thecorrection factors provide a correspondence between the distancesextracted in step 292, which are related to the scanning distancesbetween the different regions of fringe contrast, and the actualdistances between different interfaces of the sample (e.g., a thicknessof a thin film) as a function of the experimental conditions used tocollect the data in step 290, including at least the optical spectrumand the illumination geometry as input parameters.

For example, in the limit of very low NA and white light illumination,the correction approaches dividing the apparent thickness given by thescanning distance in step 292 by the group-velocity index of refraction.In the opposite limit, of very high NA and monochromatic illumination,the correction approaches multiplying the apparent thickness given bythe scanning distance in step 292 by the index of refraction.

The interferometer in step 290 may include any of the followingfeatures: a spectrally narrow-band light source with a high numericalaperture (NA) objective; a spectrally broad band light source; acombination of a high NA objective and a spectrally broadband source; aninterferometric microscope objectives, including oil/water immersion andsolid immersion types, in e.g. Michelson, Mirau or Linnik geometries; asequence of measurements at multiple wavelengths; unpolarized light; andpolarized light, including linear, circular, or structured. For example,structured polarized light may involve, for example, a polarizationmask, generating different polarizations for different segments of theillumination or imaging pupils, so as to reveal polarization-dependentoptical effects attributable to surface characteristics.

FIG. 3 shows a scanning interferometer of the Linnik type. Illuminationlight 102 from a source (not shown) is partially transmitted by a beamsplitter 104 to define reference light 106 and partially reflected bybeam splitter 104 to define measurement light 108. The measurement lightis focused by a measurement objective 110 onto a test sample 112 (e.g.,a sample comprising a thin single- or multi-layer film of one or moredissimilar materials). Similarly, the reference light is focused by areference objective 114 onto a reference mirror 116. Preferably, themeasurement and reference objectives have common optical properties(e.g., matched numerical apertures). Measurement light reflected (orscattered or diffracted) from the test sample 112 propagates backthrough measurement objective 110, is transmitted by beam splitter 104,and imaged by imaging lens 118 onto a detector 120. Similarly, referencelight reflected from reference mirror 116 propagates back throughreference objective 114, is reflected by beam splitter 104, and imagedby imaging lens 118 onto a detector 120, where it interferes with themeasurement light.

For simplicity, FIG. 3 shows the measurement and reference lightfocusing onto particular points on the test sample and reference mirror,respectively, and subsequently interfering on a corresponding point onthe detector. Such light corresponds to those portions of theillumination light that propagate perpendicular to the pupil planes forthe measurement and reference legs of the interferometer. Other portionsof the illumination light ultimately illuminate other points on the testsample and reference mirror, which are then imaged onto correspondingpoints on the detector. In FIG. 3, this is illustrated by the dashedlines 122, which correspond to the chief rays emerging from differentpoints on the test sample that are imaged to corresponding points on thedetector. The chief rays intersect in the center of the pupil plane 124of the measurement leg, which is the back focal plane of measurementobjective 110. Light emerging from the test sample at an angle differentfrom that of the chief rays intersect at a different location of pupilplane 124.

In preferred embodiments, detector 120 is a multiple element (i.e.,multi-pixel) camera to independently measure the interference betweenthe measurement and reference light corresponding to different points onthe test sample and reference mirror (i.e., to provide spatialresolution for the interference pattern).

A scanning stage 126 coupled to test sample 112 scans the position ofthe test sample relative to measurement objective 110, as denoted by thescan coordinate ζ in FIG. 3. For example, the scanning stage can bebased on a piezoelectric transducer (PZT). Detector 120 measures theintensity of the optical interference at one or more pixels of thedetector as the relative position of the test sample is being scannedand sends that information to a computer 128 for analysis.

Because the scanning occurs in a region where the measurement light isbeing focused onto the test sample, the scan varies the optical pathlength of the measurement light from the source to the detectordifferently depending on the angle of the measurement light incident on,and emerging from, the test sample. As a result, the optical pathdifference (OPD) from the source to the detector between interferingportions of the measurement and reference light scale differently withthe scan coordinate ζ depending on the angle of the measurement lightincident on, and emerging from, the test sample. In other embodiments ofthe invention, the same result can be achieved by scanning the positionof reference mirror 116 relative to reference objective 114 (instead ofscanning test sample 112 relative to measurement objective 110).

This difference in how OPD varies with the scan coordinate ζ introducesa limited coherence length in the interference signal measured at eachpixel of the detector. For example, the interference signal (as afunction of scan coordinate) is typically modulated by an envelopehaving a spatial coherence length on the order of λ/2 (NA)², where λ isthe nominal wavelength of the illumination light and NA is the numericalaperture of the measurement and reference objectives. To increase thelimited spatial coherence, the objectives in the scanning interferometerpreferably define a large numerical aperture, e.g., greater than about0.7 (or more preferably, greater than about 0.8, or greater than about0.9). The interference signal can also be modulated by a limitedtemporal coherence length associated with the spectral bandwidth of theillumination source. Depending on the configuration of theinterferometer, one or the other of these limited coherence lengtheffects may dominate, or they may both contribute substantially to theoverall coherence length.

Another example of a scanning interferometer is the Mirau-typeinterferometer shown in FIG. 4.

Referring to FIG. 4, a source module 205 provides illumination light 206to a beam splitter 208, which directs it to a Mirau interferometricobjective assembly 210. Assembly 210 includes an objective lens 211, areference flat 212 having a reflective coating on a small centralportion thereof defining a reference mirror 215, and a beam splitter213. During operation, objective lens 211 focuses the illumination lighttowards a test sample 220 through reference flat 212. Beam splitter 213reflects a first portion of the focusing light to reference mirror 215to define reference light 222 and transmits a second portion of thefocusing light to test sample 220 to define measurement light 224. Then,beam splitter 213 recombines the measurement light reflected (orscattered) from test sample 220 with reference light reflected fromreference mirror 215, and objective 211 and imaging lens 230 image thecombined light to interfere on detector (e.g., a multi-pixel camera)240. As in the system of FIG. 3, the measurement signal(s) from thedetector is sent to a computer (not shown).

The scanning in the embodiment of FIG. 4 involves a piezoelectrictransducer (PZT) 260 coupled to Mirau interferometric objective assembly210, which is configured to scan assembly 210 as a whole relative totest sample 220 along the optical axis of objective 211 to provide thescanning interferometry data I(ζ,h) at each pixel of the camera.Alternatively, the PZT may be coupled to the test sample rather thanassembly 210 to provide the relative motion there between, as indicatedby PZT actuator 270. In yet further embodiments, the scanning may beprovided by moving one or both of reference mirror 215 and beam splitter213 relative to objective 211 along the optical axis of objective 211.

Source module 205 includes a spatially extended source 201, a telescopeformed by lenses 202 and 203, and a stop 204 positioned in the frontfocal plane of lens 202 (which coincides with the back focal plane oflens 203). This arrangement images the spatially extended to source ontothe pupil plane 245 of Mirau interferometric objective assembly 210,which is an example of Koehler imaging. The size of stop controls thesize of the illumination field on test sample 220. In other embodiments,the source module may include an arrangement in which a spatiallyextended source is imaged directly onto the test sample, which is knownas critical imaging. Either type of source module may be used with theLinnik-type scanning interferometry system of FIG. 1.

In much of the analysis herein, it is assumed that the polarizationstate of the light in the pupil plane is random, i.e., comprised ofapproximately equal amounts of both s polarizations (orthogonal to theplane of incidence) and p (orthogonal to the plane of incidence)polarizations. Alternative polarizations are possible, including pure spolarization, such as may be realized by means of a radial polarizerplaced in the pupil plane (e.g., in the back-focal plane of themeasurement object in the case of a Linnik interferometer and in theback focal plane of the common objective in the Mirau interferometer).Other possible polarizations include radial p polarization, circularpolarization, and modulated (e.g. two states, one following the other)polarization for ellipsometric measurements. In other words, opticalproperties of the test sample can be resolved not only with respect totheir angle- or wavelength-dependence, but also with respect to theirpolarization dependence or with respect to a selected polarization. Suchinformation may also be used to improve the accuracy of thin filmstructure characterization.

To provide such ellipsometry measurements, the scanning interferometrysystem may include a fixed or variable polarizer in the pupil plane.Referring again to FIG. 4, the Mirau-type interferometry system, forexample, includes polarization optics 280 in the pupil plane to select adesired polarization for the light incident on, and emerging from thetest sample. Furthermore, the polarization optics may be reconfigurableto vary the selected polarization. The polarization optics may includeone or more elements including polarizers, waveplates, apodizationapertures, and/or modulation elements for selecting a givenpolarization. Furthermore, the polarization optics may be fixed,structured or reconfigurable, for the purpose of generating data similarto that of an ellipsometer. For example, a first measurement with aradially-polarized pupil for s polarization, followed by aradially-polarized pupil for p polarization. In another example, one mayuse an apodized pupil plane with linearly polarized light, e.g., a slitor wedge, which can be rotated in the pupil plane so as to direct anydesired linear polarization state to the object, or a reconfigurablescreen such as a liquid crystal display.

We now describe a theoretical model for the scanning interferometrysignal. The model is the basis for providing the correction factors instep 298 of FIG. 2.

A full physical model can be very elaborate, taking into account thepartial coherence of the light source, polarization mixing in theinterferometer, the imaging properties of high-NA objectives, and theinteraction of electric field vectors at high angles of incidence and inthe presence of discontinuous surface features. We elect here tosimplify the model by assuming a randomly-polarized, low-coherenceextended source and a smooth surface that does not scatter or diffractincident light. The total signal is the incoherent sum of theinterference contributions of all of the ray bundles passing through thepupil plane of the objective and reflecting from the object surface atan incident angle ψ, as shown in FIG. 5.

Following the usual two-beam interference analysis, the interferencecontribution for a single ray bundle through the optical system isproportional tog(β,k,ζ)=R+Z+2√{square root over (RZ)} cos[2βk(h−ζ)+(υ−ω)],  (1)where Z is the effective object intensity reflectivity, including e.g.the transmissivity of the beamsplitter, and R is the effective referencereflectivity, including both the beamsplitter and the reference mirror,and we assume a refractive index of 1 for the ambient medium. Thedirectional cosine β for an incident angle ψ isβ=cos(ψ)  (2)and the angular wavenumber k for a source wavelength λ isk=(2π/λ)  (3)

The phase term in Eq. (1) has a contribution ω for the object path inthe interferometer, including any phase change on reflection from theobject surface (including underlying layer(s)), and a contribution υ forthe reference path, including the reference mirror and other optics inthe objective. In the general case, Z, R, υ, ω all vary with directionalcosine β and angular wavenumber k.

The total interference signal for a single scan position ζ is theintegral over all points in the pupil plane and over all wavelengths forthe ray bundle contributions g (β,k,ζ):

$\begin{matrix}{{I(\zeta)} = {\int_{0}^{\infty}{\int_{0}^{1}{{g\left( {\beta,k,\zeta} \right)}{U(\beta)}{V(k)}\beta\mspace{7mu}{\mathbb{d}\beta}\ {\mathbb{d}k}}}}} & (4)\end{matrix}$where U (β) is the intensity distribution in the pupil plane of theobjective and V (k) is the optical spectrum distribution. The extraweighting factor β in Eq. (4) follows from a cos(ψ) term attributable tothe projection angle and a sin(ψ) term for the diameter of the annulusof width dψ in the pupil plane:cos(ψ)sin(ψ)dψ=−βdβ  (5)

We assume that the objective obeys the Abbé sine condition as shown inFIG. 5.

Certain simplifying assumptions often permit direct evaluation of Eq.(4). The most common simplification is to assume a point source in thecenter of the pupil plane (U=0 for β≠0), equivalent to a very low NAillumination, and a gaussian spectrum. In the more general case of anextended source and a more complicated source spectrum, Eq. (4) impliesa numerical integration.

In preferred embodiments, the modeling can be further simplified byfrequency analysis to produce a more computationally efficient way ofsimulating the interference intensity signal I(ζ). For most applicationsof interest in common height-scanning interferometric microscopes, themost rapidly varying factor in the integrand of Eq. (4) as a function ofk and β is the quasi-periodic interference contribution g (β,k,ζ). Thisfactor in turn is modulated most rapidly by the product 2βk in the phaseterm, which we can redefine physically as the spatial frequency{circumflex over (κ)} of the interference contribution g(β,k,ζ)generated by scanning orthogonally to the sample surface:{circumflex over (κ)}=2βk  (6)

This spatial frequency {circumflex over (κ)} is the angular rate ofchange of the phase term of g(β,k,ζ) as a function of the scancoordinate ζ. In the integration, various combinations of β and k resultin the same spatial frequency {circumflex over (κ)}. One path tosimplifying Eq. (4), therefore, is to recast the calculation in termsequivalent to these spatial frequencies. As we shall show, the numericalcalculation of the intensity signal I(ζ) can then be more efficientlyexpressed as a fast Fourier Transform of the frequency-domain spectrumq(K) of the signal, where K is the frequency coordinate of thetransformed data.

The first step in the simplifying analysis is the somewhatcounter-intuitive step of Fourier Transforming Eq. (4), leading to atriple integral that defines q (K):

$\begin{matrix}{{q(K)} = {\int_{0}^{\infty}{\int_{0}^{1}{{U(\beta)}{V(k)}\left\{ {\int_{- \infty}^{\infty}{{g\left( {\beta,k,\zeta} \right)}{\exp\left( {{\mathbb{i}K}\;\zeta} \right)}\ {\mathbb{d}\zeta}}}\  \right\}\beta{\mathbb{d}\beta}\ {{\mathbb{d}k}.}}}}} & (7)\end{matrix}$After expansion of the cosine term in g(β,k,ζ) in the usual way2 cos({circumflex over (κ)}ζ+ . . . )=exp(i{circumflex over (κ)}ζ+ . . .)+exp(−i{circumflex over (κ)}ζ− . . . )  (8)

and using the Dirac delta function

$\begin{matrix}{{{\delta\left( {K \pm \hat{\kappa}} \right)} = {\int_{- \infty}^{\infty}{{\exp\left\lbrack {\left( {K \pm \hat{\kappa}} \right){\mathbb{i}}\;\zeta} \right\rbrack}\ {\mathbb{d}\zeta}}}},} & (9)\end{matrix}$

the inner integral over ζ evaluates to

$\begin{matrix}{{{\int_{- \infty}^{\infty}{{g\left( {\beta,k,\zeta} \right)}{\exp\left( {{\mathbb{i}}\; K\;\zeta} \right)}\ {\mathbb{d}\zeta}}} = {{{\delta(K)}\left( {R + Z} \right)} + {{\delta\left( {K - \hat{\kappa}} \right)}\sqrt{RZ}{\exp\left\lbrack {{{\mathbb{i}}\;\hat{\kappa}\; h} + {{\mathbb{i}}\left( {\upsilon - \omega} \right)}} \right\rbrack}} + {{\delta\left( {K + \hat{\kappa}} \right)}\sqrt{RZ}{\exp\left\lbrack {{{- {\mathbb{i}}}\hat{\kappa}\; h} - {{\mathbb{i}}\left( {\upsilon - \omega} \right)}} \right\rbrack}}}}\mspace{11mu}} & (10)\end{matrix}$

The δ functions underscore that the mathematically general frequencies Kof the Fourier decomposition relate to the spatial frequency {circumflexover (κ)} defined by Eq. (6). A logical change of variables in Eq. (7)for the second inner integral at constant k is thereforeβ={circumflex over (κ)}/2k  (11)dβ=d{circumflex over (κ)}/2k  (12)

Eq. (7) after using Eq. (10) then becomes

$\begin{matrix}{{q(K)} = {{\int_{0}^{\infty}{\int_{0}^{2\; k}{{\delta(K)}\left( {R + Z} \right)\Gamma\ {\mathbb{d}\hat{\kappa}}\ {\mathbb{d}k}}}} + {\int_{0}^{\infty}{\int_{0}^{2\; k}{{\delta\left( {K - \hat{\kappa}} \right)}\sqrt{RZ}{\exp\left\lbrack {{{\mathbb{i}}\hat{\kappa}\; h} + {{\mathbb{i}}\left( {\upsilon - \omega} \right)}} \right\rbrack}\Gamma\ {\mathbb{d}\hat{\kappa}}\ {\mathbb{d}k}}}} + {\int_{0}^{\infty}{\int_{0}^{2\; k}{{\delta\left( {K + \hat{\kappa}} \right)}\sqrt{RZ}{\exp\left\lbrack {{{- {\mathbb{i}}}\hat{\kappa}\; h} - {{\mathbb{i}}\left( {\upsilon - \omega} \right)}} \right\rbrack}\Gamma\ {\mathbb{d}\hat{\kappa}}\ {\mathbb{d}k}}}}}} & (13)\end{matrix}$

where we have gathered the weighting terms asΓ({circumflex over (κ)},k)=U[β({circumflex over (κ)},k)]V(k){circumflexover (κ)}/4k ².  (14)Although for compactness we have not noted the dependencies explicitlyin Eq. (13), it is understood that Z, R, υ, ω, Γ all vary with spatialfrequency {circumflex over (κ)} and wavelength k.

The presence of dirac functions in the integrands of Eq. (13) eventuallyleads to the following simplification:

$\begin{matrix}{{q(K)} = {{{\delta(K)}{\int_{0}^{\infty}{\int_{\hat{\kappa}/2}^{\infty}{\left( {R + Z} \right)\Gamma\ {\mathbb{d}k}\ {\mathbb{d}\hat{\kappa}}}}}} + {{H(K)}{\exp\left( {{\mathbb{i}}\;{Kh}} \right)}{\int_{K/2}^{\infty}{\left\{ {\sqrt{RZ}{\exp\left\lbrack {{\mathbb{i}}\left( {\upsilon - \omega} \right)} \right\rbrack}\ \Gamma} \right\}_{\hat{\kappa} = {+ K}}{\mathbb{d}k}}}} + {{H\left( {- K} \right)}{\exp\left( {{- {\mathbb{i}}}\;{Kh}} \right)}{\int_{{- K}/2}^{\infty}{\left\{ {\sqrt{RZ}{\exp\left\lbrack {- {{\mathbb{i}}\left( {\upsilon - \omega} \right)}} \right\rbrack}\Gamma} \right\}_{\hat{\kappa} = {- K}}\ {{\mathbb{d}k}.}}}}}} & (15)\end{matrix}$

where H is the unitless Heaviside step function defined by

$\begin{matrix}{{H(u)} = \left\{ \begin{matrix}0 & {{{for}\mspace{14mu} u} < 0} \\1 & {otherwise}\end{matrix} \right.} & (16)\end{matrix}$The calculation of the frequency-domain representation of theinterference signal has now been reduced to one double integral for theDC term (K=0), and to single integrals over k for all other spatialfrequencies (K≠0). This is a substantial simplification in terms of thenumber of numerical evaluations.

The incoherent superposition model accommodates polarization by summingthe resulting Fourier components q(K) for s and p polarizationcontributions. Writing this explicitely for fully random polarization,q(K)=q _(s)(K)+q _(p)(K),  (17)where the s and p subscripts in Eq. (17) refer to Eq. (15) with all ofthe relevant parameters calculated for the corresponding polarizationstate, including the sample reflectivity, the beamsplitter, and so on.

The final calculation of the interference signal is now an inverseFourier Transform

$\begin{matrix}{{I(\zeta)} = {\int_{- \infty}^{\infty}{{q(K)}{\exp\left( {{- {\mathbb{i}}}\; K\;\zeta} \right)}\ {\mathbb{d}K}}}} & (18)\end{matrix}$Although this is another integral, it can be evaluated by a numericalFFT and is therefore of low computational burden.

One benefit of Eq. (15) is computational efficiency. To illustrate this,the integrals are replaced with sums as follows:

$\begin{matrix}{{q_{0} = {\sum\limits_{k \geq 0}^{\;}\;{\sum\limits_{k > {K/2}}^{\;}\;{\left( {R + Z} \right)\Gamma}}}}\ldots} & (19) \\{{q\left( {K > 0} \right)} = {{\exp\left( {{\mathbb{i}}\;{Kh}} \right)}{\sum\limits_{k > {K/2}}^{\;}\;{\sqrt{RZ}{\exp\left\lbrack {{\mathbb{i}}\left( {\upsilon - \omega} \right)} \right\rbrack}{\Gamma.}}}}} & (20)\end{matrix}$

If the N discrete samples for I(ζ) are spaced by an increment ζ_(step),there will be N/2+1 positive spatial frequencies starting from zero andrising to N/2 cycles per data trace, spaced by an increment

$\begin{matrix}{K_{step} = {\frac{2\;\pi}{N\;\zeta_{step}}.}} & (21)\end{matrix}$Unless the spectral bandwidth and or the range of incident angles isexceptionally large, only a fraction of the total frequency range isneeded to fully characterize the signal. There are therefore only a fewrelevant K values for which q(K) is nonzero. For example, if we acquiredata at a nominal rate of eight camera frames per interference fringe,this is a spatial frequency of N/8 cycles per data trace in a numericalFFT. Assuming quite safely that the source bandwidth is no greater thanthe nominal mean wavelength itself, there would be <N/8 values tocalculate using Eq. (20). In the example following Eq. (5), if there areN=256 individual scan positions, the number of relevant K values will be32, and if we employ 64 angular wavenumbers k in the numericalintegration, there are 2048 calculations each for Eqs. (19) and (20), orof order 200× fewer complex calculations then a direct numericalevaluation of Eq. (4). Even after factoring in the cost of the inverseFourier Transform, this substantial relief in computation makes it morepractical to perform full-field simulations of signals in low coherenceinterferometry.

It is worthwhile considering the limit cases of collimated white light(temporal coherence limit) and high-NA monochromatic illumination(spatial coherence limit). Along with verifying Eq. (13), these limitcases provide insight into the frequency-domain portrait of theinterference signal.

For both of these limit cases, as a first simplifying step, let usassume that the phase contribution (υ−ω)=0 for all K, k and that thereflectivities R, Z are independent of incident angle and wavelength, sothat the integrals in Eq. (13) simplify to

$\begin{matrix}{{q(K)} = {{{\delta(K)}\left( {R + Z} \right){\int_{0}^{\infty}{\int_{\hat{\kappa}/2}^{\infty}{{\Gamma\left( {\hat{\kappa},k} \right)}\ {\mathbb{d}k}\ {\mathbb{d}\hat{\kappa}}}}}} + {{H(K)}{\exp\left( {{\mathbb{i}}\;{Kh}} \right)}\sqrt{RZ}{\int_{K/2}^{\infty}{{\Gamma\left( {K,k} \right)}\ {\mathbb{d}k}}}} + {{H\left( {- K} \right)}{\exp\left( {{- {\mathbb{i}}}\;{Kh}} \right)}\sqrt{RZ}{\int_{{- K}/2}^{\infty}{{\Gamma\left( {{- K},k} \right)}{\mathbb{d}k}}}}}} & (22)\end{matrix}$Now we have only to handle integrals involving the weighting factorΓ({circumflex over (κ)},k) defined in Eq. (14).

One limit case is for collimated white light. The illumination angle forthis case is ψ=0 and consequently the pupil plane function isU(β)=δ(β−1).  (23)Rewriting in terms of k,U(K,k)=δ(K/2k−1).  (24)Using the mathematical identity

$\begin{matrix}{{\delta\left\lbrack {f(k)} \right\rbrack} = \frac{\delta\left( {k - \xi} \right)}{{{{\mathbb{d}f}/{\mathbb{d}k}}}_{k = \xi}}} & (25)\end{matrix}$

where ξ is the root of f(k), we have

$\begin{matrix}{{\Gamma\left( {K,k} \right)} = {\frac{K^{2}}{8}\frac{V(k)}{k^{2}}{{\delta\left( {k - {K/2}} \right)}.}}} & (26)\end{matrix}$

The integrals simplify via the delta function to

$\begin{matrix}{{q(K)} = {{{\delta(K)}\frac{\left( {R + Z} \right)}{2}{\int_{0}^{\infty}{{V\left( {\hat{\kappa}/2} \right)}\ {\mathbb{d}\hat{\kappa}}}}} + {{H(K)}\frac{\sqrt{RZ}{\exp\left( {{\mathbb{i}}\;{Kh}} \right)}}{2}{V\left( {K/2} \right)}} + {{H\left( {- K} \right)}\frac{\sqrt{RZ}{\exp\left( {{- {\mathbb{i}}}\;{Kh}} \right)}}{2}{{V\left( {{- K}/2} \right)}.}}}} & (27)\end{matrix}$Looking at the positive, nonzero portion of the spectrum, we see thatthe magnitude of the Fourier coefficients are directly proportional tothe source spectral distribution V:|q(K>0)|∝V(k)  (28)where at normal incidence the frequency K is twice the angularwavenumber k:k=K/2. Eq. (28) is the familiar result that there is aFourier transform relationship between the interference signal and theemission spectrum of the white light source.

The opposing limit is an extended monochromatic light source. This maybe represented by a delta-function spectrum for a nominal angularwavenumber k₀:V(k)=δ(k−k ₀).  (29)Eq. (22) readily simplifies to

$\begin{matrix}{{q(K)} = {{{\delta(K)}\left( {R + Z} \right){\int_{0}^{\infty}{\hat{\kappa}{U\left( {{\hat{\kappa}/2}\; k_{0}} \right)}\ {\mathbb{d}\hat{\kappa}}}}} + {{H(K)}{H\left( {k_{0} - {K/2}} \right)}\frac{{\exp\left( {{\mathbb{i}}\;{Kh}} \right)}\sqrt{RZ}}{4\; k_{0}^{2}}{{KU}\left( {{K/2}\; k_{0}} \right)}} + {{H\left( {- K} \right)}{H\left( {k_{0} + {K/2}} \right)}\frac{{\exp\left( {{- {\mathbb{i}}}\;{Kh}} \right)}\sqrt{RZ}}{{4\; k_{0}^{2}}\;}{{KU}\left( {{{- K}/2}\; k_{0}} \right)}}}} & (30)\end{matrix}$Looking once again at the positive, nonzero portion of the spectrum, wesee that the magnitude of the Fourier coefficients are now proportionalto the function U weighted by the spatial frequency K:|q(K>0)|∝βU(β)  (31)where the spatial frequency K is proportional to the directional cosineβ: β=K/2k₀. This reveals a Fourier transform relationship between theinterference signal and the cosine of the illumination angle.

Most successful interference microscope profilometry applications todayare for single material surfaces. For these cases, using the Fresnelequations, one can calculate an amplitude reflectivity z that for thesimplest case of an ideal beamsplitter fully defines the reflectivity Zand phase shift ω for the measurement path:Z(β,k)=|z(β,k)|²  (32)ω(β,k)=arg[z(β,k)]  (33)

Here again, the incoherent superposition model accommodates thedependency of the reflection coefficient z on polarization by summingthe resulting Fourier components for s and p polarization contributions(Eq. (17)).

A more challenging situation for an interference microscope is an objectcomprised of partially-transparent thin film layers. Such samples arebeing delivered with increasing frequency to the optical metrology labas thin film nanostructures such as MEMS devices, flat panel displaypixels, and patterned semiconductors extend their dominance in hightechnology applications.

A straightforward example is a single-layer film deposited on asubstrate. The amplitude reflectivity z becomes

$\begin{matrix}{{z\left( {\beta,k} \right)} = \frac{\vartheta + {\vartheta^{\prime}{\exp\left\lbrack {2\;{\mathbb{i}}\; k\; L\;{\beta^{\prime}(\beta)}n^{\prime}} \right\rbrack}}}{1 + {\vartheta\;\vartheta^{\prime}{\exp\left\lbrack {2\;{\mathbb{i}}\;{kL}\;{\beta^{\prime}(\beta)}n^{\prime}} \right\rbrack}}}} & (34)\end{matrix}$where L is the thickness of the film, n′ is the index of the film, θ isthe reflectivity of the air-film interface, θ′ is the reflectivity ofthe film-substrate interface, andβ′(β)=√{square root over (1−(1−β²)/n′ ²)}.  (35)is the directional cosine of propagation within the film.

The model can be similarly extended to structures with multiple films.

The interference signal generation for a thin film is quite interestingand has some surprises, especially with high-NA objectives. FIGS. 6( a)and 6(b) compares computer simulations of the model of an interferencemicroscope for a L=2-μm layer of a hypothetical dielectric film of indexn′=2 on a substrate of index 4. FIG. 6( a) shows that with the whitelight illumination, there are two distinct signals corresponding to thetwo interfaces. The film appears to be twice the physical thickness L,the optical thickness being close to Ln′. The signals are well separatedand one can analyze each of them separately to determine the profile ofeach interface. In prior-art systems, the technique for finding thephysical thickness is to divide by the index of refraction n′. The modelshows, however, that the correction is more accurately the groupvelocity index n′_(G) of the film material, which takes into account thedispersion in the material. Note that the group velocity index isdefined as the derivative of the wavenumber with respect to frequency.The distinction can be very important. For example, if the film iscommon silicon dioxide, using the group velocity index as proposedherein improves the measurement accuracy with respect to the prior artby 4%.

FIG. 6( b) shows that for monochromatic light and a high-NA objective,there are again two signals, but this time they are much closer togetherthan in FIG. 6( a), the optical thickness being close to L/n′. Here theapparent thickness is actually inferior to the physical thickness byabout a factor of two. Use of the prior-art Ln′ formula in this casewould lead to an even more serious error in determining the correctphysical thickness.

We have also verified the model experimentally. We viewed asolid-surface, SiC flat using a 100×, 0.78 NA Mirau objective in amicroscope with a white-light LED having a 62-nm emission bandwidth. Weassumed (and attempted experimentally) a uniform illumination of thepupil, thus U(β)=1 within the NA of the objective and outside thecentral Mirau obscuration, and is zero elsewhere. The interferenceobjective was treated as having a perfect 50/50 beamsplitter with afixed value for the reference path phase shift υ, and we allowed thesignal strength and an average value of the phase offset ω to beadjustable parameters in comparing experiment to theory. FIG. 7( a)shows excellent agreement with experimental data, indicating that thesimple incoherent superposition model is sufficient for simulating themain features of interference signals in practical applications.

For a thin film example, we elected the same 100×, 0.78 NA Mirauobjective as for FIG. 7( a), but exchanged the light source for a narrow27-nm bandwidth LED centered at 498 nm. The sample is thin film standardof 1025 nm of SiO₂ on Si. Once again we observe in FIG. 7( b) asatisfying agreement between experiment and theory. The results are soclose, that the difference is difficult to quantify by inspection of thesignal itself. A comparison in the frequency domain, shown in FIGS. 8(a) and 8(b), indicate characteristic features of thin films, includingnonlinearities in Fourier magnitude and phase that can be associatedwith material index and film thickness.

Referring again to FIG. 2, the model is used to provide thecorrespondence between the scanning distance between the regions of thefringe contrast in the interferometry signal and the actual distancebetween the interfaces in the sample that give rise to the differentregions of fringe contrast. As shown above, the model takes into accountthe geometrical and spectral properties of the interferometer. Forexample, the model can be used to determine the separation betweenregions of fringe contrast for each of a series of different thicknessesfor a thin film sample, for each of different illumination settings fora particular interferometer. The results of the model can then be usedto provide a correspondence between the actual thickness of a thin filmsample based on the separation of the between the regions of fringecontrast from an experimental interferometry signal as a function of theilluminations settings (e.g., NA and illumination bandwidth) used tocollect the signal. The computer used to analyze the experimental signalmay also be used to perform the numerical calculations for the model.Alternatively, the results from the modelling can be done in advance,with the resulting correspondence being stored in the computer used toanalyze the experimental data in the form of scaling factors, look-uptables, and/or functions.

In some embodiments, the correspondence between the distance between theregions of the fringe contrast in the interferometry signal and theactual distance between the interfaces in the sample can be a simplescaling factor that is parametrized by the NA and the frequencybandwidth of the interferometer. For example, as described above, for ahigh-NA objective with a very narrow illumination frequency spectrum,one would correct for refraction distortions by multiplying by the indexof refraction. We can understand this by likening the geometric limitson coherence to a focus effect. Using the paraxial lens formula, onefinds that the position of best focus is shifted when entering from avacuum into a material of index n′. The best focus position iscoincident with the position of equal optical path length for themultiply-angled rays reflecting from the surface, and is consequentlythe position of highest fringe contrast. On the other hand, as describedabove, in the limit of high-bandwidth and low-NA, the scaling factor isthe inverse of the group velocity index. In other words, the distancebetween the regions of fringe contrast in the interferometry signal isdivided by the group velocity index to determine the actual distancebetween the sample interfaces.

As described above, the scaling factors are stored in a look-up table(e.g., a storage database in an electronic processor). For example, theexpected results for a 60-nm bandwidth, 500-nm center wavelength with a0.35-NA objective generates an apparent thickness of approximately7n′L/8, as shown in FIG. 9. A close match of specific experimentalconditions to these parameters implies that the true physical thicknessL is 8/7n′ times the apparent thickness.

In further embodiments, the correspondence may differ from such linearscaling, and may involve a non-linear relationship between the scanningdistance between the regions of the fringe contrast in theinterferometry signal and the actual distance between the sampleinterfaces for each of different illumination conditions.

In some cases, the specific interferometer used to collect the data instep 290 may have a fixed illumination frequency spectrum, but mayimplement various objectives with different numerical aperturesdepending on the specific application. In such cases, the correctionfactors provided in step 298, while based on the illumination frequencyspectrum, may only be parametrized according the different numericalapertures of the objectives because only one illumination frequencyspectrum is used. So, in some embodiments, for example, the inputparameter for the illumination frequency spectrum is fixed, and need notbe specified. Conversely, in other cases, the specific interferometerused to collect the data in step 290 may have a fixed NA and a variableillumination frequency spectrum (e.g., interchangeable LED sources), inwhich case, the correspondence between the distance between the regionsof the fringe contrast in the interferometry signal and the actualdistance between the sample interfaces, while based on the illuminationgeometry, may only be parametrized according the illumination frequencyspectrum.

In another aspect of the invention, the illumination settings can beselected to suppress the regions of fringe contrast for underlyinglayer(s) to allow more accurate analysis of the fringe contrast regionfor the top surface using, for example, conventional analysistechniques. As a result, an accurate surface profile of the top surfacecan be determined, even for complex samples having one or moreunderlying layers. Typically, this is possible, at least for visiblewavelengths, with NAs greater than 0.5, and preferable greater than 0.7.This is illustrated in the simulation shown in FIG. 10 for an L=2-μmthick film of index n′=2 deposited on a substrate of index 4, viewedwith a 500-nm center wavelength, 0.8 NA and 200-nm bandwidth. Thecombination of broad spectral bandwidth and high NA suppresses theunderlying reflection. As a result, one can profile the top surfaceonly, free of unwanted interference effects. More generally, theillumination settings necessary to suppress the contrast fringes fromunderlying layer can be determined using the theoretical model describedabove. The surface profile can be determined based on the relativechange in the position of the fringe contrast region in theinterferometry signal for different sample locations, using theconventional techniques described in the background. The techniquedescribed in commonly owned U.S. patent application Ser. No. 10/941,651entitled “SURFACE PROFILING USING AN INTERFERENCE PATTERN MATCHINGTEMPLATE” by Peter J. de Groot and filed Sep. 15, 2004, which wasincorporated by reference and described above, can also be used.

Typically, large interference objectives having such large NAs have acorrespondingly large magnification (e.g., larger than about 40×), whichin turn reduces the field of view. In many applications, however, thesuppression phenomenon is desired, by not at the expense of a largefield of view. For example, in some applications, a sample may havemultiple thin film regions separated laterally by regions having nounderlying layers. In such cases it can be desirable to image an arealarge enough to cover multiple thin film regions or other landmarks. Toachieve this result, interference objectives should be selected thathave large NA (e.g., greater than 0.5, and preferably greater than 0.7),but not so large magnification (e.g., less than 10×). While suchobjectives are not common for interferometers, they are common in otherfields such as telescope eye-pieces, and could be easily adapted for usein an interference microscope.

In preferred embodiments, the model can further include system errorsfor the interference microscope. As an example, a nonlinear chromaticdispersion resulting from an imbalance in refractive materials betweenthe measurement and reference paths can be modeled asυ(k)=υ₀+(k−k ₀)²

  (36)where

is the second-order phase dependence of υ). This aberration leads to abroadening of the fringe contrast envelope. A similar envelopebroadening for interference patterns that are limited by spatialcoherence can be attributed to a nonlinear dependence of the systemphase υ on the directional cosine β, which can result from opticalaberrations.

Another example of a system imperfection is the signal integration timeof the camera, which has the effect of averaging the signal over a rangeof scan positions. This often-called “integrating bucket” may be modeledas the convolution of a rectangular “boxcar” window with the signal. Inthe frequency domain, the convolution becomes the product of the Fouriercoefficients q with a sync function:

$\begin{matrix}{{{B(K)} = \frac{\sin\left( {K\;{\zeta_{step}/2}} \right)}{K\;{\zeta_{step}/2}}},} & (37)\end{matrix}$where ζ_(step) is the scan increment between data frames, as previouslydefined for Eq. (21). The effect of this time integration is to dampenthe contribution from the higher spatial frequencies, as well as toreduce overall fringe contrast.

Furthermore, many system imperfections are field dependent. A relevantexample is linear dispersion in the system phase υ, which changes thephase of the underlying carrier in the interference signal with respectto the fringe contrast envelope. The field dependence of the systemphase behavior complicates the determination of fringe order. Modelingthis phenomenon over the full image field is an example of wherecomputational efficiency of Eq. (19) and (20) is a substantial benefit.

The data processing procedures described above can be applied to a largerange of low coherence interferometry systems. For example, the lightsource in the interferometer may be any of: an incandescent source, suchas a halogen bulb or metal halide lamp, with or without spectralbandpass filters; a broadband laser diode; a light-emitting diode; acombination of several light sources of the same or different types; anarc lamp; any source in the visible spectral region; any source in theIR spectral region, particularly for viewing rough surfaces & applyingphase profiling; any source in the UV spectral region, particularly forenhanced lateral resolution; and any source or combination of sourceshaving a net spectral bandwidth broader than 0.1% of the meanwavelength. Furthermore, the scanning system may be: driven by any of apiezo-electric device, a stepper motor, and a voice coil; implementedopto-mechanically or opto-electronically rather than by pure translation(e.g., by using any of liquid crystals, electro-optic effects, strainedfibers, and rotating waveplates); any of a driver with a flexure mountand any driver with a mechanical stage, e.g. roller bearings or airbearings. Also, the interferometer optics may form any of: aninterferometric microscope employing, e.g., a Mirau or Michelsonobjective lens; a Linnik, a Twyman Green system; a Fizeau interferometeremploying a filtered or structured source spectrum so as to providecoherence peaks far from zero OPD; a fiber interferometer; and a MachZehnder, particularly for profiling transparent media. Finally, the dataanalysis may involve any of: frequency domain analysis (FDA);peak-fringe analysis; dynamic filtering to extract the fringe visibilityin real time; a least-squares technique to extract fringe visibility andphase at the same time; and fringe visibility analysis followed by phaseanalysis, potentially including a separate measurement for phase with amodified source spectrum.

The analysis steps described above can be implemented in hardware orsoftware, or a combination of both. The methods can be implemented incomputer programs using standard programming techniques following themethod and figures described herein. Program code is applied to inputdata to perform the functions described herein and generate outputinformation. The output information is applied to one or more outputdevices such as a display monitor. Each program may be implemented in ahigh level procedural or object oriented programming language tocommunicate with a computer system. However, the programs can beimplemented in assembly or machine language, if desired. In any case,the language can be a compiled or interpreted language. Moreover, theprogram can run on dedicated integrated circuits preprogrammed for thatpurpose.

Each such computer program is preferably stored on a storage medium ordevice (e.g., ROM or magnetic diskette) readable by a general or specialpurpose programmable computer, for configuring and operating thecomputer when the storage media or device is read by the computer toperform the procedures described herein. The computer program can alsoreside in cache or main memory during program execution. The analysismethod can also be implemented as a computer-readable storage medium,configured with a computer program, where the storage medium soconfigured causes a computer to operate in a specific and predefinedmanner to perform the functions described herein.

The methods and systems described above can be particularly useful inany application in which one is interested in the thickness and/orsurface profiles of complex samples, e.g., thin film and multilayersamples. Some exemplary applications are described below.

Semiconductor Applications

It is presently of considerable interest in the semiconductor industryto make quantitative measurements of surface topography. Due to thesmall size of typical chip features, the instruments used to make thesemeasurements typically must have high spatial resolution both paralleland perpendicular to the chip surface. Engineers and scientists usesurface topography measuring systems for process control and to detectdefects that occur in the course of manufacturing, especially as aresult of processes such as etching, polishing, cleaning and patterning.

For process control and defect detection to be particularly useful, asurface topography measuring system should have lateral resolutioncomparable to the lateral size of typical surface features, and verticalresolution comparable to the minimum allowed surface step height.Typically, this requires a lateral resolution of less than a micron, anda vertical resolution of less than 1 nanometer. It is also preferablefor such a system to make its measurements without contacting thesurface of the chip, or otherwise exerting a potentially damaging forceupon it, so as to avoid modifying the surface or introducing defects.Further, as it is well-known that the effects of many processes used inchip making depend strongly on local factors such as pattern density andedge proximity, it is also important for a surface topography measuringsystem to have high measuring throughput, and the ability to sampledensely over large areas in regions which may contain one or manysurface features of interest.

Chemical Mechanical Polishing Applications

It is becoming common among chip makers to use the so-called ‘dualdamascene copper’ process to fabricate electrical interconnects betweendifferent parts of a chip. This is an example of a process which may beeffectively characterized using a suitable surface topography system.The dual damascene process may be considered to have six parts: (1) aninterlayer dielectric (ILD) deposition, in which a layer of dielectricmaterial (such as a polymer, or glass) is deposited onto the surface ofa wafer (containing a plurality of individual chips); (2) chemicalmechanical polishing (CMP), in which the dielectric layer is polished soas to create a smooth surface, suitable for precision opticallithography, (3) a combination of lithographic patterning and reactiveion etching steps, in which a complex network is created comprisingnarrow trenches running parallel to the wafer surface and small viasrunning from the bottom of the trenches to a lower (previously defined)electrically conducting layer, (4) a combination of metal depositionsteps which result in the deposition of copper trenches and vias, (5) adielectric deposition step in which a dielectric is applied over thecopper trenches and vias, and (6) a final CMP step in which the excesscopper is removed, leaving a network of copper filled trenches (andpossibly vias) surrounded by dielectric material.

Referring to FIG. 11 a, a device 500 is exemplary of the a filmstructure resulting from the deposition of a dielectric 504 over copperfeatures 502 deposited on a substrate 501. The dielectric 504 has anon-uniform outer surface 506 exhibiting height variations therealong.

Interference signals obtained from device 500 can include interferencepatterns resulting from surface 506, an interface 508 between copperfeatures 502 and dielectric 504, and an interface 510 between substrate501 and dielectric 504. The device 500 may include a plurality of otherfeatures that also generate interference patterns. Referring to FIG. 11b, a device 500′ illustrates the state of device 500 after the final CMPstep. The upper surface 506 has been planarized to a surface 506′, andinterface 508 may now be exposed to the surroundings. Interface 510 atthe substrate surface remains intact. Device performance and uniformitydepends critically on monitoring the planarization of surface 504. It isimportant to appreciate that the polishing rate, and therefore theremaining copper (and dielectric) thickness after polishing, dependsstrongly and in a complex manner on the polishing conditions (such asthe pad pressure and polishing slurry composition), as well as on thelocal detailed arrangement (i.e., orientation, proximity and shape) ofcopper and surrounding dielectric regions. Hence, portions of surface506 over copper elements 502 may etch at different rates than otherportions of surface 506. Additionally, once interface 508 of copperelements 502 is exposed, the dielectric and copper elements may exhibitdifferent etch rates.

This ‘position dependent polishing rate’ is known to give rise tovariable surface topography on many lateral length scales. For example,it may mean that chips located closer to the edge of a wafer onaggregate are polished more rapidly than those located close to thecenter, creating copper regions which are thinner than desired near theedges, and thicker than desired at the center. This is an example of a‘wafer scale’ process nonuniformity—i.e., one occurring on length scalecomparable to the wafer diameter. It is also known that regions whichhave a high density of copper trenches polish at a higher rate thannearby regions with low copper line densities. This leads to aphenomenon known as ‘CMP induced erosion’ in the high copper densityregions. This is an example of a ‘chip scale’ processnon-uniformity—i.e., one occurring on a length scale comparable to (andsometimes much less than) the linear dimensions of a single chip.Another type of chip scale nonuniformity, known as ‘dishing’, occurswithin single copper filled trench regions (which tend to polish at ahigher rate than the surrounding dielectric material). For trenchesgreater than a few microns in width dishing may become severe with theresult that affected lines later exhibit excessive electricalresistance, leading to a chip failure.

CMP induced wafer and chip scale process nonuniformities are inherentlydifficult to predict, and they are subject to change over time asconditions within the CMP processing system evolve. To effectivelymonitor, and suitably adjust the process conditions for the purpose ofensuring that any nonuniformities remain within acceptable limits, it isimportant for process engineers to make frequent non-contact surfacetopography measurements on chips at a large number and wide variety oflocations. This is possible using embodiments of the interferometrymethods and systems described above.

In some embodiments one or more spatial properties, e.g., the topographyof surface 506 and/or the thickness of dielectric 504, are monitored byobtaining low coherence interference signals from the structure beforeand/or during CMP. Based on the spatial properties, the polishingconditions can be changed to achieve the desired planar surface 506′.For example, the pad pressure, pad pressure distribution, polishingagent characteristics, solvent composition and flow, and otherconditions can be determined based on the spatial properties. After someperiod of polishing, the spatial property can again be determined andthe polishing conditions changed as needed. The topography and/orthickness is also indicative of the end-point at which, e.g., surface504′ is achieved. Thus, the low coherence interference signals can beused to avoid depressions caused by over polishing different regions ofthe object. The low coherence interference methods and systems areadvantageous in this respect because spatial properties of the device,e.g., the relative heights of the surface of the dielectric (a) overcopper elements 502 and (b) over substrate surface 510 but adjacentcopper elements 502 can be determined even in the presence of themultiple interfaces.

Solder Bump Processing

Referring to FIGS. 12 a and 12 b, a structure 550 is exemplary of astructure produced during solder bump processing. Structure 550 includesa substrate 551, regions 502 non-wettable by solder, and a region 503wettable by solder. Regions 502 have an outer surface 507. Region 503has an outer surface 509. Accordingly, an interface 505 is formedbetween regions 502 and substrate 501.

During processing a mass of solder 504 is positioned in contact withwettable region 503. Upon flowing the solder, the solder forms a securecontact with the wettable region 503. Adjacent non-wettable regions 502act like a dam preventing the flowed solder from undesirable migrationabout the structure. It is desirable to know spatial properties of thestructure including the relative heights of surfaces 507, 509 and thedimensions of solder 504 relative to surface 502. As can be determinedfrom other discussions herein, structure 550 includes a plurality ofinterfaces that may each result in an interference pattern. Overlapbetween the interference patterns prevents accurate determinate of thespatial properties using known interference techniques. Application ofthe systems and methods discussed herein allow the spatial properties tobe determined.

Spatial properties determined from structure 550 can be used to changemanufacturing conditions, such as deposition times for layers 502,503and the amount of solder 504 used per area of region 503. Additionally,heating conditions used to flow the solder can also be changed based onthe spatial properties to achieve adequate flow and or prevent migrationof the solder.

Liquid Crystal Displays

Referring to FIG. 13, a passive matrix LCD 450 is composed of severallayers. The main parts are two glass plates 452,453 connected by seals454. A polarizer 456 is applied to the front glass plate 453 in order topolarize incoming light in a single direction. The polarized lightpasses through the front glass plate 453. An Indium Tin Oxide (ITO)layer 458 is used as an electrode. A passivation layer 460, sometimescalled hard coat layer, based on SiOx is coated over the ITO 458 toelectrically insulate the surface. Polyimide 462 is printed over thepassivation layer 460 to align the liquid crystal fluid 464. The liquidcrystal fluid is sensitive to electric fields and changes orientationwhen an electric field is applied. The liquid crystal is also opticallyactive and rotates the polarization direction of the incoming light. Thecell gap Δg, i.e., thickness of the liquid crystal layer 464, isdetermined by spacers 466, which keep the two glass plates 452,453 at afixed distance. When there is no electric potential from the front plate453 to the rear plate 452, the polarized light is rotated 90° as itpasses through the liquid crystal layer 464. When an electric potentialis applied from one plate to the other plate the light is not rotated.After the light has passed through the liquid crystal layer 464, itpasses through another polyimide layer 468, another hard coat layer 470,a rear ITO electrode 472, and the rear glass plate 452. Upon reaching arear polarizer 474, the light either transmitted through or absorbed,depending on whether or not it has been rotated 90°. The cell 450 mayinclude filters 476 or other colorizing elements to provide a colordisplay.

The cell gap Δg determines to a great extent the optoelectricalproperties of the LCD, e.g., the contrast ratio and brightness. Cell gapcontrol during manufacturing is critical to obtaining uniform, qualitydisplays. The actual cell gap may differ from the dimensions of spacers466 because, during assembly, pressure or vacuum is applied to introducethe liquid crystal medium, seals 454 cure and may change dimensions, andthe added liquid crystal medium generates capillary forces betweenplates 452,453. Both before and after adding the liquid crystal medium464, surfaces 480,482 of plates 452,453 reflect light that results in aninterference pattern indicative of the cell gap Δg. The low coherencenature of the interference signal either itself or in combination withthe described interference signal processing techniques can be used tomonitor properties of the cell including the cell gap Δg duringmanufacture even in the presence of interfaces formed by other layers ofthe cell.

An exemplary method can include obtaining a low coherence interferencesignal including interference patterns indicative of the cell gap Δgprior to adding layer 464. The cell gap (or other spatial property ofthe cell) is determined from the interference patterns and can becompared to a specified value. Manufacturing conditions, e.g., apressure or vacuum applied to plates 452,453 can be changed to modifythe cell gap Δg if a difference between the specified value and thedetermined cell gap exceeds tolerances. This process can be repeateduntil achieving the desired cell gap. Liquid crystal medium is thenintroduced into the cell. The amount of liquid crystal medium to beadded can be determined from the measured spatial property of the cell.This can avoid over- or underfilling the cell. The filling process canalso be monitored by observing interference signals from the surfaces480,482. Once the cell has been filed, additional low coherenceinterference patterns are obtained to monitor the cell gap Δg (or otherspatial property). Again, the manufacturing conditions can be changed sothat the cell gap is maintained or brought within tolerances.

Laser Scribing and Cutting

Lasers can be used to scribe objects in preparation for separatingdifferent, concurrently manufactured structures, e.g., microelectronicsstructures. The quality of separation is related to the scribingconditions, e.g., laser focus size, laser power, translation rate of theobject, and scribe depth. Because the density of features of thestructure may be large, the scribe lines may be adjacent thin film orlayers of the structures. Interfaces associated with the thin film orlayers may create interference patterns that appear when interferometryis used to determine the scribe depth. The methods and systems describedherein can be used to determine the scribe depth even in the presence ofsuch adjacent films or layers.

An exemplary method can include scribing one or more electronicstructures and separating the structures along the scribe lines. Beforeand/or after separation, low coherence interference signals can be usedto determine the depth of scribe. Other scribing conditions are known,e.g., laser spot size, laser power, translation rate. The scribe depthcan be determined from the interference signals. The quality ofseparation as a function of the scribing conditions, including thescribe depth, can be determined by evaluating the separated structures.Based on such determinations, the scribing conditions necessary toachieve a desired separation quality can be determined. During continuedmanufacturing, low coherence interference signals can be obtained fromscribed regions to monitor the process. Scribing conditions can bechanged to maintain or bring the scribe properties within tolerances.

A number of embodiments of the invention have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the invention.

1. A method comprising: using a microscope having a numerical apertureto illuminate a sample with test light having a frequency spectrum,where the sample includes multiple interfaces; combining test lightreflected from the sample with reference light reflected from areference surface to form combined light and directing the combinedlight to a multi-element detector; acquiring a signal for each elementof the multi-element detector while scanning the sample relative to themulti-element detector, wherein during the scanning the referencesurface remains fixed with respect to the multi-element detector and thesignal for each element comprises multiple regions of amplitudevariation, each region of amplitude variation corresponding to one ofthe interfaces; and determining a thickness profile or a surface heightprofile of the sample based on the numerical aperture, the frequencyspectrum, and a separation between the corresponding regions ofamplitude variation in the signal for each element.
 2. The method ofclaim 1, wherein determining the thickness profile or the surface heightprofile comprises determining a distance between at least a pair of theinterfaces at multiple spatial locations of the sample.
 3. The method ofclaim 1, wherein the region of amplitude variation corresponds to thescan position where an optical path difference between test lightreflected from the corresponding interface and the reference light atthe multi-element detector is zero.
 4. The method of claim 1, whereinthe numerical aperture is greater than about 0.5.
 5. The method of claim1, wherein determining the distance between at least one pair ofinterfaces comprises providing information about a correspondencebetween the distance between the pair of interfaces and the separationbetween the corresponding regions of amplitude variation in the signalsfor different settings of the numerical aperture and the frequencyspectrum.
 6. The method of claim 5, wherein the correspondence isrepresented as a function or a look-up table that uses the informationabout the numerical aperture and the frequency spectrum as inputparameters.
 7. The method of claim 5, wherein the correspondence isbased on a theoretical model for the interferometer that uses theinformation about the numerical aperture and the frequency spectrum asinput parameters.
 8. The method of claim 1, wherein the distance betweenthe pair of interfaces is determined by determining an estimate for thedistance between the pair of interfaces corresponding to the separationbetween the two regions of amplitude variation, and correcting theestimate based on the information about the numerical aperture and thefrequency spectrum.
 9. The method of claim 8, wherein the correction ofthe initial estimate comprises decreasing the estimate by a scale factorthat increases with a group velocity index of a film corresponding to aregion between the pair of interfaces.
 10. The method of claim 8,wherein the correction of the initial estimate comprises increasing theestimate by a scale factor that increases with a refractive index of thefilm.
 11. The method of claim 1, wherein the sample is a thin filmsample, and the pair of interfaces is a top and bottom surface of thefilm.
 12. The method of claim 11, wherein the sample has the film atsome spatial locations and not others.
 13. The method of claim 1,wherein the sample comprises a spacer element in a liquid crystal cell.14. The method of claim 1, wherein the sample comprises a solder bump.15. A system, comprising: a microscope comprising an objective having anumerical aperture and comprising a reference surface and being arrangedto illuminate a sample with test light having a frequency spectrum andto combine test light reflected from the sample with reference lightreflected from the reference surface to form combined light; amulti-element detector positioned to receive the combined light; a stageconfigured to position the sample to receive the test light, where thesystem is arranged to scan the sample relative to the multi-elementdetector while the reference surface remains fixed with respect to themulti-element detector; an electronic processor programmed to receiveand analyze a signal from each element of the multi-element detectorwhile the system scans the sample and to determine a thickness profileor a surface height profile of the sample, wherein each signal comprisesmultiple regions of amplitude variation corresponding to multipleinterfaces in the sample, and the thickness profile or the surfaceheight profile is determined based on a separation between thecorresponding regions of amplitude variation in the signal for eachelement, the numerical aperture of the microscope, and the frequencyspectrum.
 16. The system of claim 15, wherein objective has a numericalaperture greater than about 0.5.
 17. The system of claim 15, wherein themicroscope has a magnification less than 10×.
 18. The system of claim15, wherein the microscope comprises a source having an adjustablefrequency spectrum, the source being configured to provide the testlight to the microscope.
 19. The system of claim 18, wherein theadjustable source comprises a plurality of light sources havingdifferent emission spectrums.
 20. The system of claim 15, wherein thestage is configured to position a liquid crystal display substrate toreceive the test light.
 21. The system of claim 15, wherein the stage isconfigured to position a semiconductor wafer to receive the test light.